Definition Distribution function
The distribution function describes the dependence between a random variable and its probabilities, i.e., it indicates the probability with which a random variable takes a specific value.
Example: A football player is injured during training. Based on experience, it takes about two to seven days for him to recover and be able to play again. The random variable describes the number of days until recovery. Based on the recovery of other football players that suffered the exact same injury, we know that if fewer than two days have passed, the probability that the player has recovered is 0% since this injury takes at least two days to heal. If three days have passed, the probability that the player recovered is low but existing, 5%. When four days have passed, the chances of being healed from the injury increase further to 20%. After seven days from the injury, the probability of healing is 100%.
Mathematically, the distribution function is the integral of the density function. Possible kinds of distribution functions are the normal distribution, the uniform distribution, and the binomial distribution.
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